Detection Thresholds and Bias Correction in Polarized Intensity

George S.J., Stil J.M., Keller B.W. – arxiv:1106.5362

Detection thresholds in polarized intensity and polarization bias correction are investigated for surveys where the polarization information is obtained from RM synthesis. Considering unresolved sources with a single rotation measure, a detection threshold of 8 \sigma_{QU} applied to the Faraday spectrum will retrieve the RM with a false detection rate less than $10^{-4}$, but polarized intensity is more strongly biased than Ricean statistics suggest. For a detection threshold of 5 \sigma_{QU}, the false detection rate increases to ~4%, depending also on $\lambda^2$ coverage and the extent of the Faraday spectrum. Non-Gaussian noise in Stokes Q and U due to imperfect imaging and calibration can be represented by a distribution that is the sum of a Gaussian and an exponential. The non-Gaussian wings of the noise distribution increase the false detection rate in polarized intensity by orders of magnitude. Monte-Carlo simulations assuming non-Gaussian noise in Q and U, give false detection rates at 8 \sigma_{QU} similar to Ricean false detection rates at 4.9 \sigma_{QU}.

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